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arXiv · 2011.07708

An explicit computation of the Hecke operator and the ghost conjecture

Nha Xuan Truong
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Abstract

In this paper, we investigate the Hecke operator at p = 5 and show that the upper minors of the matrix have non zero corank and, interestingly, follow the same ghost pattern in the Ghost conjecture of Bergdall and Pollack. Due to this facts, we conjecture that the slope of Hecke action in this case can be computed using an appropriate variant of ghost series. Assume this result, we achieve an upper bound for the slopes that is similar to the Gouvea's (k-1)/(p+1) conjecture.

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BibTeXRIS

Nha Xuan Truong. 2023-05-16. An explicit computation of the Hecke operator and the ghost conjecture. https://doi.org/10.1007/s40993-023-00447-9

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